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A Philosophical Approach to Quantum Field Theory PDF

275 Pages·2018·5.223 MB·English
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A PHILOSOPHICAL APPROACH TO QUANTUM FIELD THEORY This text presents an intuitive and robust mathematical image of fundamental particle physics based on a novel approach to quantum field theory, which is guided by four carefully motivated metaphysical postulates. In particular, the book explores a dissipative approach to quantum field theory, which is illustrated for scalar field theory and quantum electrodynamics and proposes an attractive explanation of the Planck scale in quantum gravity. Offering a radically new perspective on this topic, the book focuses on the conceptual foundations of quantum field theory and ontological questions. It also suggests a new stochastic simulation technique in quantum field theory, which is complementary to existing ones. Encouraging rigor in a field containing many mathematical subtleties and pitfalls, this text is a helpful companion for students of physics and philosophers interested in quantum field theory, and it allows readers to gain an intuitive rather thanaformalunderstanding. hans christian o¨ttinger is Professor of Polymer Physics at ETH Zu¨rich. His research is focused on developing a general framework of nonequilibrium thermodynamicsasatoolfordescribingdissipativeclassicalandquantumsystems. A PHILOSOPHICAL APPROACH TO QUANTUM FIELD THEORY HANS CHRISTIAN O¨ TTINGER SwissFederalInstituteofTechnology UniversityPrintingHouse,CambridgeCB28BS,UnitedKingdom OneLibertyPlaza,20thFloor,NewYork,NY10006,USA 477WilliamstownRoad,PortMelbourne,VIC3207,Australia 314–321,3rdFloor,Plot3,SplendorForum,JasolaDistrictCentre,NewDelhi–110025,India 79AnsonRoad,#06–04/06,Singapore079906 CambridgeUniversityPressispartoftheUniversityofCambridge. ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitof education,learning,andresearchatthehighestinternationallevelsofexcellence. www.cambridge.org Informationonthistitle:www.cambridge.org/9781108415118 DOI:10.1017/9781108227667 ©HansChristianO¨ttinger2017 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. Firstpublished2017 PrintedintheUnitedKingdombyClays,StIvesplc AcataloguerecordforthispublicationisavailablefromtheBritishLibrary. LibraryofCongressCataloging-in-PublicationData Names:O¨ttinger,HansChristian,1958–author. Title:Aphilosophicalapproachtoquantumfieldtheory/HansChristianO¨ttinger (SwissFederalInstituteofTechnology,Zu¨rich). Description:Cambridge,UnitedKingdom;NewYork,NY:CambridgeUniversityPress,2017.| Includesbibliographicalreferencesandindex. Identifiers:LCCN2017035063| ISBN9781108415118(Hardback;alk.paper)|ISBN1108415113(Hardback;alk.paper) Subjects:LCSH:Quantumfieldtheory.|Physics–Philosophy.|Knowledge,Theoryof. Classification:LCCQC174.45.O892017|DDC530.14/3–dc23 LCrecordavailableathttps://lccn.loc.gov/2017035063 ISBN978-1-108-41511-8Hardback CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyof URLsforexternalorthird-partyinternetwebsitesreferredtointhispublication anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain, accurateorappropriate. ToRicarda, whomeanstheworldtome Contents Preface pagexi Acknowledgments xiii 1 ApproachtoQuantumFieldTheory 1 1.1 PhilosophicalContemplations 2 1.1.1 ImagesofNature 3 1.1.2 SpaceandTime 11 1.1.3 Infinity 19 1.1.4 Irreversibility 23 1.1.5 OntheMeasurementProblem 34 1.1.6 ApproachestoQuantumFieldTheory 38 1.2 MathematicalandPhysicalElements 49 1.2.1 FockSpace 50 1.2.2 Fields 55 1.2.3 Dynamics 57 1.2.4 QuantitiesofInterest 69 1.2.5 Renormalization 76 1.2.6 Symmetries 87 1.2.7 Expansions 89 1.2.8 Unravelings 92 1.2.9 Summary 103 2 ScalarFieldTheory 110 2.1 SomeBasicEquations 111 2.1.1 FreeDissipativeEvolution 111 2.1.2 PerturbationTheory 113 2.2 Propagator 115 2.2.1 Second-OrderPerturbationExpansion 116 2.2.2 GoingtotheLimits 121 vii viii Contents 2.2.3 RelativisticCovariance 126 2.2.4 OnShellRenormalization 129 2.3 VertexFunction 132 2.3.1 Four-TimeCorrelationFunctions 133 2.3.2 APrimaryCorrelationFunction 134 2.3.3 CoreCorrelationFunctions 137 2.4 SummaryandDiscussion 138 3 QuantumElectrodynamics 141 3.1 TheDiracEquation 142 3.1.1 WaveEquationsforFreeParticles 143 3.1.2 RelativisticCovariance 144 3.1.3 PlanarWaveSolutions 146 3.1.4 InteractionwithElectromagneticFields 150 3.1.5 From3+1to1+1Dimensions 151 3.2 MathematicalImageofQuantumElectrodynamics 153 3.2.1 FockSpace 153 3.2.2 Fields 156 3.2.3 HamiltonianandCurrentDensity 159 3.2.4 SchwingerTerm 162 3.2.5 BRSTQuantization 163 3.2.6 QuantumMasterEquation 174 3.3 SchwingerModel 176 3.3.1 FockSpace 177 3.3.2 Fields 178 3.3.3 HamiltonianandCurrentDensity 180 3.3.4 SchwingerTerm 182 3.3.5 BRSTQuantization 182 3.3.6 ExactSolution 184 3.3.7 FermionsandBosonsinOneSpaceDimension 191 3.4 ConfrontationwiththeRealWorld 197 3.4.1 FreePropagators 198 3.4.2 ScatteringProblems 200 3.4.3 MagneticMomentoftheElectron 210 4 Perspectives 220 4.1 TheNatureofQuantumFieldTheory 220 4.1.1 TheImage 220 4.1.2 ImplicationsforOntology 222 4.2 OpenMathematicalProblems 225 4.3 FutureDevelopments 227 Contents ix AppendixA AnEfficientPerturbationScheme 229 AppendixB PropertiesofDiracMatrices 239 AppendixC Baker–Campbell–HausdorffFormulas 241 References 243 Indexes AuthorIndex 251 SubjectIndex 254

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